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Asset Returns and Economic Growth

A note for the next time I teach graduate macro:

A fall in the rate of economic growth--whether because of slower labor-force growth or slower growth in technology and organization--should carry with it a reduction in rates of profit and asset returns. Why? The intuition is clear: slower growth in labor, technology, or organization all reduce this generation's supply of effective labor relative to the capital stock provided by last generation's saving and investment. Effective labor becomes relatively scarcer, and capital becomes relatively more abundant. Thus the wage paid to an effective unit of labor rises, and rates of profit and asset returns fall: supply and demand.

However, it is especially interesting that one of the standard models--the Ramsey-Cass-Koopmans model as set out in Romer's Advanced Macroeconomics--predicts that while rates of return should fall when labor productivity growth falls, reductions in labor force growth have no effect on rates of profit and asset returns. In the R-C-K model, labor-force growth takes the form of an increase in the number of members of the representative household. The utility of the representative household is equal to the number of its members times a function (with declining marginal utility) of consumption per capita. Thus big households are better at turning consumption into utility than small ones. A R-C-K household that controlled its own fertility would choose to grow in size as rapidly as possible (even if the real wage its members earned were zero) in order to grasp the possibility of becoming more efficient at transforming goods into utility.

Thus it turns out that in the R-C-K model a reduction in the labor force growth rate has two effects. First, it reduces the relative supply of effective labor in the future. Second, it reduces the efficiency of the household in the future at turning consumption goods into utility. The first effect raises the relative abundance of capital and causes rates of return to fall. The second effect diminishes incentives to save, reduces the relative abundance of capital, and causes rates of return to rise. It turns out that they exactly offset each other.

But is this a result we want--to say that a reduction in the rate of population growth reduces savings rates because households recognize that their future versions will be less efficient at turning goods into utility because they will be smaller in number? I suspect not, especially once one recognizes that the representative agent is a fiction and that the households doing the bulk of the saving are in all likelihood not the same as the households doing the bulk of the growing.

There is a general lesson here: these models are clean, elegant, powerful, and have lots of hidden subtleties that commit you to implicit assumptions you probably do not want to make. Inspect them carefully.